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13 Dec 2014, 00:33

viktorija wrote:

Can anybody explain why the answer is E?

The answer is E because the question stem doesn't specify which 2 angles are equal, angle A or angle C could both be equal to 40. Also, the 2 statements mean the same- AD as angle bisector itself means ab x bd = ac x dc

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17 Dec 2014, 06:55

raj44 wrote:

viktorija wrote:

Can anybody explain why the answer is E?

The answer is E because the question stem doesn't specify which 2 angles are equal, angle A or angle C could both be equal to 40. Also, the 2 statements mean the same- AD as angle bisector itself means ab x bd = ac x dc

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The answer is E because the question stem doesn't specify which 2 angles are equal, angle A or angle C could both be equal to 40. Also, the 2 statements mean the same- AD as angle bisector itself means ab x bd = ac x dc

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You can also understand this property in the following manner. Refer the diagram below:

In the diagram, ABC is an isosceles triangle with sides AB = AC. As angles opposite the equal sides are equal we have ∠B = ∠C = \(x\). Also AD is the angle bisector of ∠A, therefore ∠BAD = ∠CAD = \(\frac{y}{2}\).

However please note that the only the angle bisector of the non-equal angle of an isosceles triangle will be perpendicular to the opposite base i.e. the non-equal side. Also AD bisects base BC i.e. BD = DC. These properties will not apply to the equal angles and the equal sides.

In case of an equilateral triangle, we know that \(x = 60\) and \(\frac{y}{2} = 30\), hence \(z = 90\). In an equilateral triangle since all angles and sides are equal, these properties would apply to any of the angles and sides.

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You can also understand this property in the following manner. Refer the diagram below:

In the diagram, ABC is an isosceles triangle with sides AB = AC. As angles opposite the equal sides are equal we have ∠B = ∠C = \(x\). Also AD is the angle bisector of ∠A, therefore ∠BAD = ∠CAD = \(\frac{y}{2}\).

However please note that the only the angle bisector of the non-equal angle of an isosceles triangle will be perpendicular to the opposite base i.e. the non-equal side. Also AD bisects base BC i.e. BD = DC. These properties will not apply to the equal angles and the equal sides.

In case of an equilateral triangle, we know that \(x = 60\) and \(\frac{y}{2} = 30\), hence \(z = 90\). In an equilateral triangle since all angles and sides are equal, these properties would apply to any of the angles and sides.